I've just done my 3rd batch of ale and prior to my other posts where I've said it's never as strong as it says on the box I've done a reading 4 weeks after secondary fermentation( after my Finings had been added and 80g of spray malt also added for carbonation ) all instructions I've read say to do your final reading after a week or so after the yeast has been added. Is this giving me a true or false reading?

Ideally, take your FG reading just before you add the priming sugar (or whatever). If you add the priming sugar, you might read a couple points high, but it's not going to be a big error. Taking an FG earlier in the process may give you a false high reading, but after a week in a normal ale fermentation you should probably be very close to FG anyway. It's not a bad idea to take an SG reading when you think it's done and then wait a few days to take an FG reading. If the FG doesn't match your previous reading, then wait another few days and repeat.

Waiting too long won't give you a false high FG reading, though.

Edit: Just saw your 2nd post. If you did a reading after 1 week, then kegged or bottled or whatever, it's quite possible that your 1 week reading was a few points high.

Ideally, take your FG reading just before you add the priming sugar (or whatever). If you add the priming sugar, you might read a couple points high, but it's not going to be a big error. Taking an FG earlier in the process may give you a false high reading, but after a week in a normal ale fermentation you should probably be very close to FG anyway. It's not a bad idea to take an SG reading when you think it's done and then wait a few days to take an FG reading. If the FG doesn't match your previous reading, then wait another few days and repeat.

Waiting too long won't give you a false high FG reading, though.

Edit: Just saw your 2nd post. If you did a reading after 1 week, then kegged or bottled or whatever, it's quite possible that your 1 week reading was a few points high.

I did 2 readings before I barrelled a couple of days apart and they were the same. They were lower than the instructions said they would be by about 4 points which is why I did another one 4 weeks later after the priming sugar was exhausted as the ale was carbonated. The reading is now what it should be but I just wondered if this is a true reading

Your final reading is whatever time it takes for the beer to be done.
Depending on the beer and yeast, it can take a lot longer than two weeks after the yeast is added.
"Final" is when it's done changing. You ideally check your reading and when it doesn't change for between readings that are three or more days apart, the fermenting is done.
You need to take readings without changing things ( no additions like priming sugar ).
Think of gravity readings as measuring the difference between the weight of pure water and water with additions.
The sugars in the unfermented wort get turned to alcohol and the density of the wort changes. You add priming sugars in any form and you are no longer comparing the final gravity to th original gravity of the wort since the composition of the wort has changed ( besides the change that the yeast causes).
What finning are you adding after it's done fermenting and ready to bottle or keg?

I did 2 readings before [...] They were lower than the instructions said they would be by about 4 points [...] another one 4 weeks later after the priming sugar was exhausted as the ale was carbonated. The reading is now what it should be

That doesn't make sense. If the earlier readings were lower than they should be, the ABV is higher. When you say "lower," are you talking about the SG (1.015 or whatever) or the ABV?

After carbonation, you will need to degas the sample to get a good reading, but that should give you a slightly high SG reading (low ABV). This just means let the sample sit around until it's flat. In any case, if your SG is dropping (ABV rising), then your last measurement is the most accurate.

If you measured gravity after the priming sugar was metabolized by the yeast, then technically you would want to add the priming sugar to your OG. But the FG is likely going to be the same number pre or post primeing sugar as long as the fermentation was allowed to complete in both cases.

The instructions said the final gravity should be 1.0009. I took 2 readings over a period of 3 days and they were both consistently 1.0012. I assumed the yeast had stopped the fermentation so I added youngs beer Finings to the bucket and let it sit for a further week before adding 80g of medium spray malt to the barrel before siphoning the beer into it. Another 4 weeks later I took another reading ( I did indeed let the beer in the test tube go flat overnight ) the reading this time was now 1.0009. My original gravity was 1.0042.